Hindawi Publishing Corporation
Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 469769, 9 pages
doi:10.1155/2012/469769
Research Article
Predictive Models for Maximum Recommended Therapeutic Dose
of Antiretroviral Drugs
Michael Lee Branham,1 Edward A. Ross,2 and Thirumala Govender1
1 School
2 School
of Pharmacy and Pharmacology, University of KwaZulu-Natal, Durban 4001, South Africa
of Medicine, University of Florida, Gainesville, FL 32601, USA
Correspondence should be addressed to Michael Lee Branham, malimahweh@gmail.com
Received 11 September 2011; Revised 4 November 2011; Accepted 18 November 2011
Academic Editor: John Hotchkiss
Copyright © 2012 Michael Lee Branham et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
A novel method for predicting maximum recommended therapeutic dose (MRTD) is presented using quantitative structure
property relationships (QSPRs) and artificial neural networks (ANNs). MRTD data of 31 structurally diverse Antiretroviral drugs
(ARVs) were collected from FDA MRTD Database or package inserts. Molecular property descriptors of each compound, that is,
molecular mass, aqueous solubility, lipophilicity, biotransformation half life, oxidation half life, and biodegradation probability
were calculated from their SMILES codes. A training set (n = 23) was used to construct multiple linear regression and back
propagation neural network models. The models were validated using an external test set (n = 8) which demonstrated that MRTD
values may be predicted with reasonable accuracy. Model predictability was described by root mean squared errors (RMSEs),
Kendall’s correlation coefficients (tau), P-values, and Bland Altman plots for method comparisons. MRTD was predicted by a
6-3-1 neural network model (RMSE = 13.67, tau = 0.643, P = 0.035) more accurately than by the multiple linear regression
(RMSE = 27.27, tau = 0.714, P = 0.019) model. Both models illustrated a moderate correlation between aqueous solubility of
antiretroviral drugs and maximum therapeutic dose. MRTD prediction may assist in the design of safer, more effective treatments
for HIV infection.
1. Introduction
Acquired immunodeficiency syndrome (AIDS) is a degenerative disease of the immune and central nervous systems caused by the human immunodeficiency virus (HIV).
There are an estimated 33.2 million people living with
HIV/AIDS globally [1–3]. Of this number, 22.5 million
are in Sub-Saharan Africa, which represents 67.8% of
the global number [3]. Antiretroviral drugs (ARVs) may
be classified as nucleoside reverse transcriptase inhibitors
(NRTIs), nucleotide reverse transcriptase inhibitors (NtRTI),
non-nucleoside reverse transcriptase inhibitors (NNRTIs),
protease inhibitors (PI), and more recently as fusion or integrase inhibitors [4, 5]. Since most ARVs have low aqueous
solubility and poor bioavailability, several alternative drug
delivery strategies have been proposed to optimize systemic
concentrations [6, 7]. The important biopharmaceutical
properties that need to be considered for effective ARV
delivery systems might include solubility, pKa, lipophilicity,
permeability, stability in biological fluids, gastrointestinal
metabolism, and where possible viral reservoir targeting [6,
8, 9]. To overcome suboptimal biopharmaceutical properties,
ARVs are often prescribed at high daily doses which increase
the occurrence of adverse side effects and toxicities [10, 11].
Combination therapy, comprising at least three anti-HIV
drugs, has become a standard treatment of AIDS [12], but
here again the potential for adverse side effects and drugrelated noncompliance increases. To address these issues,
computational methods have been used to predict doselimiting toxicities of a few antiretroviral drugs [13, 14] or to
optimize ARV formulations [15, 16]. The ability to predict
maximum therapeutic dose directly from molecular structure is both clinically and scientifically attractive in terms
of treatment management and reducing drug development
costs [17]. Unfortunately, such models for drugs used in
the treatment of AIDS do not yet exist. Accurate prediction
2
Computational and Mathematical Methods in Medicine
of the MRTD for antiretroviral type compounds would be
particularly useful in formulation studies so that clinically
relevant extrapolations on drug dissolution and permeability
can be made earlier in the drug development process [17–
20]. Several recent studies have been conducted to define
a relationship between the dose and physicochemical properties of the drug [20, 21], or to investigate the underlying
mechanisms of drug toxicity and bioaccumulation [20, 22].
Still, the prediction of optimal dose continues to challenge
pharmaceutical scientists because of its complexity and
variability between different organisms. Artificial neural networks (ANNs) have emerged as a powerful tool suitable for
processing complex relationships between molecular stimuli
and biological system responses [23]. Examples include
prediction of warfarin maintenance dose [24], gentamicin
steady-state plasma concentrations [25], skin permeability
[26], and prediction of HIV drug resistance [27]; supporting
data for these and other studies suggest the utility of neural
network modeling for predicting maximum therapeutic
doses.
We believed that since the MRTD estimates are derived
from human data, they would provide a more relevant,
accurate, and specific estimate for toxic dose levels compared
to risk assessment models based on animal data alone. In this
article, we predict the MRTD of antiretroviral drugs from
their molecular structures using relevant molecular property
descriptors and neural network software as a data mining
tool. Predictive performance of the models were evaluated
and statistically compared with the results obtained clinically
or reported in the literature. The application of predictive
models in the design of safe, effective antiretroviral drug
delivery systems is discussed.
Bias
2. Materials and Methods
2.1. Chemoinformatic Software and Modeling Tools. The
physicochemical descriptors, molecular weight (MW), aqueous solubility (ASol), and lipophilicity (AlogP) were determined using ALOGPS 2.1. Virtual Computational Chemistry
Laboratory, (http://www.vcclab.org/) [28, 29]. Bioaccumulation descriptors, log biotransformation half life (logBioHL), oxidation half life (OxidHL), and biodegradation probability (P[BD]) were determined using EPI Suite
v.410 (http://www.epa.gov/oppt/sf/tools/methods.htm) [30,
31]. All inferential statistics and MRTD data analysis was
performed using MedCalc v.12 (MedCalc Software bvba,
Belgium). Artificial neural network analysis was performed
using Tiberius Data Mining Software v.6.1.9 (Tiberius Data
Mining Software Ltd. Pty, UK).
2.2. MRTD Training and Validation Datasets. The MRTD
of 31 structurally diverse antiretroviral drugs were taken
from the FDA MRTD database or package inserts. This
“clinical MRTD” dataset was randomly split into training
and validation subsets as shown in Table 1. Subsequently,
each of the calculated descriptors and clinical MRTD values
were correlated by multiple linear regression analysis and
the results used to identify statistically significant property
descriptors. An error back propagation algorithm was used
MW
ASol
AlogP
logBioHL
Clinical MRTD
P[BD]
OxidHL
Figure 1: A neural network model was constructed with (2) hidden
neuron, (1) output variable that is Clinical MRTD, and (6) input
variables that is, OxidHL, P[BD], logBioHL, AlogP, ASol, MW. Total
number of patterns (23) were loaded in the data of which 23 were
complete and available for training. Two nonlinear neurons were
used and the model error minimization was stable for 20 minutes.
for network training, with learning rate set at 0.7. A tangent
sigmoid transfer function on the first layer and two neurons
with a nonlinear transfer function on the hidden layer were
minimalistic structures used to reduce over-fitting. Results of
MRTD versus molecular property descriptors with multiple
correlation coefficients are listed in Table 2. For the neural
network model training, correlation and error statistics are
listed in Table 3.
2.3. Model Validation and Statistical Comparisons. The predictability of each of the multiple linear regression (MLR)
and neural network (TNN) models was evaluated by a crossvalidation procedure [32]. Each model was constructed on
the basis of the same training dataset and was subsequently
used to predict the excluded test data. Statistical comparisons
were performed between the clinical MRTD and predicted
MRTD values using the root mean squared error (RMSE),
Kendall’s correlation coefficient (tau), P-value, and Bland
Altman plots for methods comparisons.
3. Results
3.1. Model Predicted versus Actual MRTD Estimates. In this
multivariable system, a quantitative relationship between
certain molecular property descriptors and maximum recommended therapeutic dose was characterized using two
datasets (i.e., MRTD and TEST). A multiple linear regression
(Table 2) and a 6-2-1-neural network model (Figure 1) for
the prediction ARVs maximum dose were constructed.
Table 1 lists summary statistics for the molecular property
descriptors and corresponding MRTD values in each dataset.
The ARVs in this study, although few in number, covered
a broad range (CV equal to 40% or greater) in terms of
the physicochemical (MW, ASol, AlogP) and bioaccumulation properties (logBioHL, OxidHL, P[BD]) included. A
significant difference in mean ASol between training set
(6.1489 g/L) and TEST set (0.436 g/L) was noted although
corresponding changes in lipophilic character were not as
great. Multiple linear regression analysis was performed with
results listed in Table 2. A statistically significant but modest
correlation between two of the six descriptors, that is, P[BD]
Computational and Mathematical Methods in Medicine
3
Table 1: Clinical MRTD data consisted of 23 training set compounds (italic) and 8 test set compounds (bold). Mean and standard deviation
statistics are shown indicating the distribution and central tendency of each molecular property descriptor.
Drug
Acyclovir
Ancitabine
Delaviridine
Didanosine
Famciclovir
Foscarnet
Indinavir
Lofexidine
Lamivudine
Rimantadine
Ribavirin
Valacyclovir
Zalcitibine
Zanamivir
Zidovudine
Saquinavir
Darunavir
Tipranavir
Ritonavir
Maraviroc
Tenofovir
Nelfinavir
Stavudine
n
mean
SD
CV%
Abacavir
Emtricitabine
Raltegravir
Nevirapine
Efavirenz
Fosamprenavir
Atazanavir
Lopiravir
n
mean
SD
CV%
MRTD (mg/kg/day)
13.30
20.00
6.67
6.67
25.00
120.00
16.70
0.040
5.00
3.33
200.00
50.00
0.0375
0.333
10.00
33.330
53.00
6.670
20.00
20.00
10.00
25.00
1.333
23.00
28.54
45.53
159.52
10.00
4.00
30.07
3.000
10.10
46.70
5.35
53.33
8.00
20.32
20.29
99.86
OxidHL
(days)
0.135
0.139
0.034
0.140
0.051
13.37
0.038
0.123
0.06
0.171
0.264
0.044
0.096
0.038
0.139
0.052
0.094
0.043
0.105
0.129
0.048
0.055
0.088
23.00
0.672
2.769
412.00
0.040
0.08
0.094
0.167
0.254
0.067
0.109
0.103
8.00
0.114
0.067
58.99
P[BD] (%)
(Rz = 0.427, P = 0.035), ASol (Rz = 0.476, P = 0.014)
and actual MRTD value is noted. MRTD values appear
to increase with P[BD], ASol, and OxidHL; but decrease
with increasing logBioHL, AlogP, or MW. The multiple
correlation coefficient (MCC = 0.7727), residual error (RSD
= 33.89), and ANOVA (P = 0.013) indicate acceptable
predictability of the multiple regression model for ARVs
0.5475
0.2005
0.0014
0.5085
0.991
0.772
0.0501
0.0792
0.0719
0.4624
0.8963
0.944
0.0909
0.8247
0.0432
0.9780
0.0001
0.0000
0.9488
0.0700
0.0016
0.6868
0.0768
23.00
0.402
0.394
97.00
0.0229
0.0566
0.0006
0.0473
0.0001
0.0007
0.0202
0.9933
8.00
0.143
0.344
241.300
logBioHL
(days)
−2.2874
−2.418
−2.3428
−1.9956
−3.6235
−2.4547
−4.6478
0.9861
−3.9261
0.4539
−2.8715
−3.3309
−3.5083
−4.4141
−3.0445
−3.9394
−1.8175
−0.0265
−4.61
−0.2247
−3.0098
−1.6709
−3.082
23.00
−2.5133
1.5738
−62.620
−2.1757
−3.7784
−2.6157
−3.7336
0.1111
−2.4135
−3.4392
−3.3281
8.00
−2.672
1.278
−47.830
AlogP (:)
ASol (g/L)
MW (Da)
−1.45
8.65
3.20
0.086
6.43
1.32
16.76
0.048
0.15
2.76
0.009
33.17
1.49
7.05
1.49
16.35
0.002
0.067
0.0002
0.0012
0.0106
1.87
0.0002
40.51
23.00
6.15
10.90
177.25
1.21
2.00
0.095
0.10
0.008
0.068
0.003
0.002
8.00
0.436
0.753
173.000
225.21
225.21
456.57
236.23
321.38
126.01
613.81
259.14
229.26
179.31
244.21
326.41
211.22
332.32
267.28
670.84
547.66
602.66
720.94
513.66
287.21
567.78
224.21
23.00
362.72
178.20
48.86
286.38
247.28
444.47
266.33
315.67
585.68
704.96
614.86
8.00
433.20
180.48
41.66
−2.62
2.77
−1.26
0.13
−1.63
3.26
3.31
−1.29
3.28
−1.92
−1.03
−1.29
−2.29
−0.1
4.04
1.76
5.71
4.24
4.3
−1.51
6.00
−0.8
23.00
0.939
2.809
299.04
0.61
−0.8
1.7
1.75
3.88
0.84
4.37
4.07
8.00
2.05
1.878
91.50
maximum dose. A multiple linear regression equation used
for the prediction of MRTD is as follows:
−34.3303 − 12.20 ∗ AlogP + 2.1249 ∗ (ASol)
+15.90 ∗ logBioHL + 0.2159 ∗ (MW)
+5.659 ∗ (OxidHL) + 46.5133 ∗ (P[BD]).
(1)
4
Computational and Mathematical Methods in Medicine
Table 2: The results of the multiple linear regression analysis for antiretroviral drugs versus MRTD. In the training, dataset only two of
the six molecular descriptors showed a statistically significant correlation with therapeutic dose, that is, P[BD] (P = 0.0349) and ASol (P =
0.0140). A multiple regression model equation coefficients are listed with there standard errors, coefficient of determination (R2 = 0.5970),
multiple correlation coefficient (MCC = 0.7727) and residual standard deviation (RSD = 33.89).
Multiple linear regression
independent variables
Constant
AlogP
ASol
logBioHL
MW
OxidHL
P[BD]
ANOVA
n = 23
Coefficient
−34.3303
−12.1995
2.1239
15.9000
0.2159
5.6589
46.5133
F-ratio = 3.9507
R2 = 0.5970
SE
6.6976
0.7697
8.0377
0.1015
2.8478
20.1746
RSD = 33.89
P-value
MCC = 0.7727
Rz
0.0873
0.0140
0.0654
0.0494
0.0643
0.0349
P = 0.013
−0.221
0.476
−0.071
−0.116
0.448
0.427
Table 3: The results of the neural network analysis for antiretroviral drugs versus MRTDs. All molecular descriptors show weak correlation
with MRTD except for ASol, OxidHL, and P[BD]. The 6-2-1 neural network model predicted training set MRTD values with high accuracy
(R2 = 0.992, MAX = 13.64, P < 0.001). No multicollinearity between independent variables was observed in the training set.
n = 23
R2 = 0.992
P < 0.001
Correlation coefficients
−0.221
0.476
−0.071
−0.116
0.448
0.427
F-ratio = 1340.73
6-2-1 neural network
Model versus clinical MRTD
Independent variables
AlogP
ASol
logBioHL
MW
OxidHL
P[BD]
ANOVA
The results of the neural network model for antiretroviral
MRTDs is shown in Table 3. All molecular descriptors show
weak correlation with MRTD except ASol, OxidHL, and
P[BD]. The 6-2-1 neural network predicted training set
MRTD values with high accuracy (R2 = 0.992, MAX =
13.64, P < 0.001). No multicollinearity between independent
variables was observed in the training set. SPSS code for the
6-2-1 neural network may be executed as follows:
COMPUTE Var1 = ((OxidHL
(−0.543086558961242)) +
3.63976611815824)
∗
+ ((Pr BD ∗ (−5.67413921537257)) +
2.81153598121711)
+ ((LogBioHL ∗ (0.40828801067156)) +
0.747514104338025)
MAX = 13.64
RMSE = 5.53
Learning rate = 0.700
R2
0.049
0.226
0.005
0.013
0.201
0.182
P < 0.001
COMPUTE Var2 = ((OxidHL ∗
(8.23491975851945E−02)) 0.551904322215974)
+ ((Pr BD ∗ (3.12529587401663)) 1.54858410557524)
+ ((LogBioHL ∗ (0.431493610228662)) +
0.790000076287146)
+ ((ALogP ∗ (−0.04107624611641)) +
6.94188559367329E−02)
+ ((Sol ∗ (4.12997852313067E−02)) −
0.836531279838639)
+ ((MW ∗ (1.05078568602304E−03)) −
0.444983569959981)
+ 9.28741349960935E-02.
+ ((ALogP ∗ (−0.848110602763694)) +
1.43330691867064)
COMPUTE Var3 = −0.535249116383622.
+ ((Sol ∗ (−2.55399028293542E−02)) +
0.517313285798853)
COMPUTE Var1 = 0.108990429907616
Execute.
∗
∗
Var1.
+ ((MW ∗ (1.40343495376914E−02)) −
5.94322423917294)
COMPUTE Var2 = 1.44376333322051
(Exp(Var2) − Exp(-Var2)) / (Exp(Var2) +
Exp(−Var2)).
+ 3.86733992096867.
COMPUTE Var3 = Var3.
Computational and Mathematical Methods in Medicine
5
Table 4: Test dataset Goodness of fit comparisons. Clinical MRTD values from 8 ARVs were using as and external test dataset the validate
model predictability. Model performance is characterized here in terms of root means squared error (RMSE), Kendall’s correlation coefficient
(tau), and Type II error probability (P-value).
MRTD
10.00
4.00
30.07
3.00
10.10
46.70
5.35
53.33
20.32
MLR
−10.6738
−23.9239
0.0628
−54.1862
−10.2863
44.0515
11.4360
42.6361
−0.1105
0.714
0.019
Execute.
COMPUTE Tiberius MRTD = ((((Var1 +
Var2 + Var3)/2.0) + 0.5) ∗ 199.9625)
+ 0.0375.
Execute.
3.2. Model Validation and Statistical Comparisons. Each of
the models was then validated using external TEST MRTD
dataset and a cross-validation procedure. Model “goodness
of fit” and predictability are summarized in Table 4. RMSE of
the 6-2-1 neural network (RMSE = 13.67) was substantially
less the multiple linear regression model (RMSE = 27.27).
Comparison of model predictivity was confirmed with TNN
having maximum squared error (SE = 601.23) compared to
MLR (SE = 3270.26). Model Figure 3 correlation with the
clinical MRTD values using Kendall’s correlation coefficient
was, however, greater for the MLR (tau = 0.714, P = 0.019)
than the resultant 6-2-1 neural network model (tau = 0.643,
P = 0.035). Bland Altman plots for methods comparison
further illustrate the predictive value of the neural network
(TNN) and multiple linear regression (MLR) models. The
upper and lower limits of agreement for the MLR (58.3,
−17.4) and TNN (29.8, −27.3) are illustrated in Figure 2.
While it can be seen that all of the differences lie between
these limits, MLR model limits of agreement were wider
than the TNN model, which were more narrow and nearly
symmetrical.
4. Discussion
MRTD values and SMILES codes for antiretroviral drugs
were collected from the FDA MRTD database which
is a highly reliable source pharmacologic activity based
on extensive clinical evidence (http://www.fda.gov/cder/).
The ALOGPS+ program was used for the calculation of
molecular mass (MW), solubility (ASol), and lipophilicity
(AlogP) without alteration. The precision and robustness of
these tools are well established in the pharmaceutical and
modeling community and its predictive power concerning
SE
427.4060
779.7441
900.4320
3270.2614
415.6012
7.0145
37.0393
114.3594
RMSE = 27.27
TNN
6.4861
3.3678
19.7700
−16.5700
−5.7782
50.7500
29.8700
64.5900
19.06
0.643
0.035
SE
12.3474
0.3996
106.0900
382.9849
252.1172
16.4025
601.2304
126.7876
RMSE = 13.67
10
10.1 30.07
Clinical MRTD
46.7
80
60
40
Predicted MRTD
Drug
Abacavir
Emtricitabine
Raltegravir
Nevirapine
Efavirenz
Fosamprenavir
Atazanavir
Lopiravir
Mean
Kendall’s tau
P-value
20
0
−20
−40
−60
3
4
5.35
53.33
MLR
TNN
Figure 2: Method comparisons graph. MRTD values predicted by
multiple linear regression (hollow squares, ) nearly traced those
values predicted by the 6-2-1 neural network (solid squares, ) as
shown. Multiple linear regression estimates for MRTD were consistently lower that those predicted by the neural network model.
the input parameters in question are published on the
company website (http://www.vcclab.com/) and cited in the
manuscript [28, 29, 33]. Independent validation of the
parameters calculated with ALOGPS has been published
[33, 34] and the estimates were found to be appropriately
accurate for the use intended. The bioaccumulation input
parameters, oxidation half life (oxidHL), log biotransformation half life (logBioHL), and biodegradation probability
(P[BD]) were calculated using the EPI Suite software which
is publically available and has been validated in hundreds
of modeling experiments for the estimated parameters. EPI
Suite software is continuously updated and the predictive
power of its latest version is always available at the website
(http://www.epa.gov/oppt/sf/tools/methods.htm). None of
6
Computational and Mathematical Methods in Medicine
60
100
+1.96 SD
58.3
60
40
Mean
20.4
20
0
−1.96 SD
−17.4
−20
−40
Clinical MRTD—predicted MRTD
Clinical MRTD—predicted MRTD
80
40
+1.96 SD
29.8
20
Mean
1.3
0
−20
−1.96 SD
−27.3
−40
−60
−60
−40
−20
0
20
40
Average of clinical MRTD and predicted MRTD
60
(a)
−20
0
20
40
60
Average of clinical MRTD and predicted MRTD
80
(b)
Figure 3: Bland Altman plot for method comparisons. Bland Altman plots are shown for (a) multiple linear regression predicted versus
clinical MRTD, and (b) neural network model predicted versus clinical MRTD. Horizontal lines are drawn at the mean difference, and at the
limits of agreement. All predicted values were within limits of agreement for both models, althought these limits were more narrow for the
neural network model estimates. The plots are useful revealing the relationship between the differences and the averages, the slight deviation
from symmetry in the multiple regression indicates some systematic bias but no possible outliers were identified.
the parameters were log-transformations of the software
output but instead used as direct input values for the training
set. Although some of the predictor values ranged over 3
orders of magnitude, this did not appear to adversely affect
comparisons of the MLR or ANN methods. Furthermore,
because of the highly diverse nature of antiretroviral compounds in terms of physicochemical descriptors and splitdata validation procedure with randomly selected training
and test sets instead of cross-validating scheme. It is our
intention to adapt the method as new ARV drugs become
listed in evolving FDA database.
We began our study looking at dose-related adverse effects of commercial antiretroviral drugs or new ARVs in
development. Although the appearance of serious longterm metabolic complications, such as cardiovascular disturbances [35], hyperlipidemia [35, 36], and diabetes, have been
extensively reported [35, 37], few reports on computational
models to predict these dose-limiting toxicities [38, 39]
can be found in the literature. A mathematical model to
predict the optimal dosing regimen for AIDS therapy has
been reported [40], but in this case, CD4+ cell counts and
knowledge of the adherence interval of individual patients is
required to adjust the dose. While the model was effective at
reducing dose-limiting toxicities in an AIDS patient population, it cannot be applied to nonapproved ARV formulations or to drugs in development. Since the overwhelming
majority of anti-HIV drugs demonstrate efficacy over a small
range of treatment doses, MRTD predicting models would be
beneficial to the drug delivery scientist who needs to design
experiments based on the most effective therapeutic dose
of the medication [41]. The MRTD is empirically derived
from human clinical trials, thus it is a direct measure of
the threshold for dose-related adverse effects in humans.
Prediction of the MRTD from molecular structure is of
importance for both new and existing drugs which may
require modifications to improve their aqueous solubility
or bioavailability in vivo. ARVs fit this description also
and are excellent subject molecules for predictive modeling
to estimate maximum dose. Unfortunately, the number of
antiretroviral drugs with established MRTD is yet small,
so the development of models specifically of ARVs is both
tedious and rare.
The molecular descriptors used in this study were selected to represent physicochemical (MW, AlogP, ASol) and
bioaccumulation (OxidHL, P[BD], logBioHL) property
influences therapeutic dose. Although molecular weight does
not strongly correlate with toxicity of most compounds, the
larger the molecular size of a compound, the smaller its
membrane permeability and diffusion coefficient become
[34]. Therefore, compounds with higher weights are less
likely to be absorbed, which limits their systemic toxicity.
Results of this study predict no correlation between molecular weight and maximum ARV dose. In contrast, bioactivity
and drug toxicity almost always increase with increasing
lipophilicity. This is due in part to the fact that lipophilic
molecules tend to cross cellular membranes more readily
increasing exposure and residence in the body. In addition,
lipophilic drugs are characterized by increased plasma protein binding, thus an assessment of lipophilicity is almost
always included in the physicochemical evaluation of a
drug because of its close association with pharmacologic,
permeability and potential bioaccumulation [42, 43]. Our
Computational and Mathematical Methods in Medicine
results here did not indicate AlogP or lipophilic character as
having any influence on ARV dose. The aqueous solubility
of a compound significantly affects its absorption and
distribution characteristics. Typically, low solubility goes
along with a poor absorption and, therefore, its systemic
toxicity reduced, however, local irritability may develop
and/or reduced elimination rates, both are characteristic of
drugs with low aqueous solubility. For highly potent drugs,
increasing solubility usually enhances the elimination rate
and lowers systemic half life, [44]. This means that for
ARVs with low aqueous solubility, some correlation with
maximum therapeutic dose (as we has shown) is likely to be
observed.
Any chemical (even water) can produce toxic side effects
in the body if allowed to accumulate to sufficiently large
concentrations. While much of the effort in bioaccumulation
modeling [43, 45] has been initiated by scientists estimating
the equilibrium distribution of chemicals between organisms and their environments (e.g., fish-water, plants-soil),
effective physicochemical property estimation routines (i.e.,
PERs) have resulted from these studies that may be applied to
similar biodistribution problems in pharmaceutical research.
For example, oxidation half life (OxidHL) is an estimate
of the molecules ability to form stable hydroxyl radicals
or to interact with such moiety under ambient conditions.
Formation of hydroxyl-radicals is often associated with doselimiting toxicities. Although in our studies, oxidation half life
was not statistically significant in the prediction of MRTD.
Another bioaccumulation descriptor, biotransformation half
life (logBioHL), is the (linearized) fraction of drug mass
in the whole body that has been metabolized per day.
Our estimates do not account for the formation of specific
metabolites which may be toxic nor do they identify specific
pathways in the process (i.e., phase I redox reactions or phase
II type conjugation reactions). Consequently, logBioHL was
not correlated with MRTD in the present study and was a
weaker bioaccumulation property descriptor in comparison
to oxidation half life or biodegradation probability P[BD].
The probability of biodegradation attempts to combine
both oxidative and biotransformation susceptibility of the
structure to give an estimate of overall persistence. P[BD]
estimates are based upon molecular fragments [46–48]
and in our investigation showed only moderate correlation
with MRTD in both multiple linear regression and neural
network models. Each of the models was evaluated for
predictive accuracy and by statistical comparison. In terms of
predictability, root mean squared errors were larger for the
multiple linear regression than the neural network model.
Some advantages of ANN over MLR models were illustrated
in the current study.
Artificial neural networks (ANNs) are biologically inspired data-mining algorithms which work by detecting the
patterns and relationships in data. We used the back propagation rule in which the neural network is trained to map
a set of input data by iterative adjustment of the weights. A
tangent sigmoid transfer function on the first layer and two
neurons with a nonlinear transfer function on the hidden
layer were minimalistic structures used to reduce overfitting.
Our training processes for TNN were allowed to run until no
7
change in RMSE was observed for 20 minutes, at which point
the model was saved. This learning method is commonly
used for neural network predictive models given doseresponse type data. However, ANNs have several limitations,
a major theoretical concern is the “black box” nature of the
output, that is, conclusions are generated without mechanistic explanations. ANNs also are limited by the quality
of their data and may need to be retrained periodically if
its performance changes over time. This is not necessarily
counterproductive, since it indicates robustness in the model
which adapts to changes in the predictive criteria. Real-time
monitoring of the training process is also important since
overtraining can easily occur, especially when the datasets are
small in size. This is may be one of the unique advantages of
real-time visualization of the data-mining process allowing
the investigator to make “intermediate evaluations” of model
predictability and then continue training until the reliability
and accuracy required of the predictions are met.
In conclusion, antiretroviral drugs are a chemically diverse class of compounds in terms of both physicochemical
properties and bioaccumulation potential. However, commercial ARVs may be categorized for predictive modeling
purposes into two groups based on aqueous solubility and
lipophilic character, in which hydrophilic compounds may
be administered at higher doses (MRTD) and prediction
of their MRTD value may be possible using simple multiple linear regression models. In contrast, the prediction
of MRTD values for antiretrovirals with poorer aqueous
solubility would be the most effective when the neural
network approach is used and when both physicochemical
and bioaccumulation property descriptors are available for
training. With regard to future studies, ANN represents a
promising tool for predicting maximum therapeutic dose,
especially for antiretroviral drugs with narrow therapeutic
index in the treatment of AIDS.
Abbreviations
AlogP:
ASol:
logBioHL:
CV:
R2 :
MLR:
MRTD:
MAX:
MW:
MCC:
OxidHL:
P[BD]:
TNN:
QSPR:
RSD:
RMSE:
SMILES:
SE:
SD:
Rz :
Calculated octanaol/water partition coefficient
Aqueous solubility
Biotransformation half life
Coefficient of variation
Coefficient of determination
Multiple linear regression
Maximum recommended therapeutic dose
maximum absolute error
Molecular weight
Multiple correlation coefficient
Oxidation half life
Biodegradation probability
Tiberius Neural Network
Quantitative Structure Property Relationships
Residual standard deviation
Root mean squared error
Simplified molecular input line entry system
Squared error
Standard deviation
Zero order correlation coefficient.
8
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